code: def sqrtrem_python(x):
      """Correctly rounded integer (floor) square root with remainder."""
      # to check cutoff:
      # plot(lambda x: timing(isqrt, 2**int(x)), [0,2000])
      if x < _1_600:
          y = isqrt_small_python(x)
          return y, x - y * y
      y = isqrt_fast_python(x) + 1
      rem = x - y * y
      # Correct remainder
      while rem < 0:
          y -= 1
          rem += 1 + 2 * y
      else:
          if rem:
              while rem > 2 * (1 + y):
                  y += 1
                  rem -= 1 + 2 * y
      return y, rem
  
imports: import math
  from bisect import bisect
  from .backend import xrange
  from .backend import BACKEND, gmpy, sage, sage_utils, MPZ, MPZ_ONE, MPZ_ZERO
label_desc: Use image node_id 14 for calling a global function with example usage: sqrtrem_python(x) and returns: y,  rem, y,  unknown